Related papers: The Charming Leading Eigenpair

We consider a matrix pencil whose coefficients depend on a positive parameter $\epsilon$, and have asymptotic equivalents of the form $a\epsilon^A$ when $\epsilon$ goes to zero, where the leading coefficient $a$ is complex, and the leading…

We study the maximum absolute value of the determinant of matrices with entries in the set of $\ell$-th roots of unity; this is a generalization of $D$-optimal designs and Hadamard's maximal determinant problem, which involves $\pm 1$…

Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…

We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from $\{0,1\}$ or $\{-1,1\}$. We describe efficient parallel algorithms for…

The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…

We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conjugate of a real matrix attract, we derive expressions for…

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some…

Riordan matrices are infinite lower triangular matrices determined by a pair of formal power series over the real or complex field. These matrices have been mainly studied as combinatorial objects with an emphasis placed on the algebraic or…

We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…

For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific…

The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…

For a fixed $n\ge2$, consider an $n\times n$ matrix $M$ whose entries are random integers bounded by $k$ in absolute value. In this paper, we examine the probability that $M$ is singular (hence has eigenvalue 0), and the probability that…

We study the eigenspace of the Laplacian matrix of a simple graph corresponding to the largest eigenvalue, subsequently arriving at the theory of modular decomposition of T. Gallai.

Let $G=(V,E)$ be an undirected graph with $n$ vertices and $m$ edges, in which each vertex $u$ is assigned an integer priority in $[1,n]$, with 1 being the "highest" priority. Let $M$ be a matching of $G$. We define the priority score of…

The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue of some non necessarily Gaussian complex Deformed Wigner Ensembles. The real model is also considered. Our approach is close to the one…

We describe the eigenvalues and the eigenspaces of the adjacency matrices of subgraphs of the Hamming cube induced by Hamming balls, and more generally, by a union of adjacent concentric Hamming spheres. As a corollary, we extend the range…

It is known that a $2\times 2$ quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher orders. In this paper a different point of view is adopted…

Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers,…

The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.